JEE Main & Advanced Physics Wave Mechanics Resonance Tube

It is used to determine velocity of sound in air by the help of a tuning fork of known frequency.

It is a closed organ pipe having an air column of variable length. When a tuning fork is brought over it's mouth. It's air column vibrates with the frequency of the fork. If the length of the air column is varied until it's natural frequency equals the frequency of the fork, then the column resonants and emits a loud note.

If \[{{l}_{1}}\] and \[{{l}_{2}}\] are lengths of first and second resonances, then we have \[{{l}_{1}}+e=\frac{\lambda }{4}\] and \[{{l}_{2}}+e=\frac{3\lambda }{4}\]

\[\Rightarrow \] \[{{l}_{2}}-{{l}_{1}}=\frac{\lambda }{2}\]\[\Rightarrow \] \[\lambda =2({{l}_{2}}-{{l}_{1}})\]

Speed of sound in air at room (temperature) \[v=n\lambda =2n({{l}_{2}}-{{l}_{1}})\]

Also \[\frac{{{l}_{2}}+e}{{{l}_{1}}+e}=3\]\[\Rightarrow \] \[{{l}_{2}}=3{{l}_{1}}+2e\] i.e. second resonance is obtained at length more than thrice the length of first resonance.